cp's OEIS Frontend

A129856 Primes that are one less than the difference between consecutive primes.

%I A129856 #33 Jan 07 2025 10:52:25
%S A129856 3,3,3,5,5,3,3,5,5,5,3,5,3,5,7,3,3,3,13,3,5,5,5,3,5,5,3,11,11,3,3,5,5,
%T A129856 5,5,5,3,13,3,3,13,5,3,5,7,5,5,3,5,7,3,7,5,3,5,7,3,3,11,7,3,7,3,5,11,
%U A129856 17,5,5,5,5,5,5,5,5,3,11,3,5,5,11,3,5,7,7,7,5,5,3,7,5,3,7,3,13,11,3,13,3,3
%N A129856 Primes that are one less than the difference between consecutive primes.
%C A129856 Might be called Prime Prime Intervals: the sequence of prime numbers that occur as 1 less than the difference between consecutive prime numbers. - _Barry Forman_, Oct 14 2016
%H A129856 Robert Israel, <a href="/A129856/b129856.txt">Table of n, a(n) for n = 1..10000</a>
%e A129856 The first 4 consecutive prime pairs are (2,3),(3,5),(5,7),(7,11). The differences - 1 are the numbers 0,1,1,3. The first three of these are not prime so 3 is the first entry in the table.
%p A129856 P:= select(isprime, [2,seq(p,p=3..10^4,2)]):
%p A129856 select(isprime, [seq(P[i]-P[i-1]-1,i=2..nops(P))]); # _Robert Israel_, Apr 18 2016
%t A129856 Select[Last[#]-First[#]&/@Partition[Prime[Range[150]],2,1]-1,PrimeQ] (* _Harvey P. Dale_, Nov 18 2013 *)
%o A129856 (PARI) diffp1p2(n) = { local(p1,p2,y); for(x=1,n, p1=prime(x); p2=prime(x+1); y=(p2-p1)- 1; if(isprime(y), print1(y",") ) ) }
%K A129856 easy,nonn
%O A129856 1,1
%A A129856 _Cino Hilliard_, May 23 2007